His research interests include major contributions to matrix inequalities, calculus of matrix functions, means of matrices, and connections between harmonic analysis, geometry and matrix analysis.

Linear matrix inequality (LMI)

An optimization-based reformulation of the Riccati equation uses Linear matrix inequalities and requires fewer assumptions.

It establishes a relation between a linear matrix inequality involving the state space constructs A, b, c and a condition in the frequency domain.

In automatic control theory, SDP's are used in the context of linear matrix inequalities.

In convex geometry, a spectrahedron is a shape that can be represented as a linear matrix inequality.

This can be concisely written as the matrix inequality:

Formation flying of multiple spacecraft via graphs, matrix inequalities, and switching, AIAA Journal of Guidance, Control, and Dynamics, (24) 2: 369-377, 2001.

This is a linear matrix inequality (LMI) feasibility test, which is a convex optimization problem.

This linear matrix inequality specifies a convex constraint on y.